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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Find the average rate of change of f(x) = 3x^2 - 2x from x = 1 to x = 4.
💡 Hint: Use the formula (f(b) - f(a)) / (b - a).
Question 2
Easy
What is the instantaneous rate of change of f(x) = 2x + 3 at x = 3?
💡 Hint: Find the derivative of the function.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the average rate of change?
- The rate at a specific point
- The overall change over an interval
- The slope of the tangent line
💡 Hint: Think about the formula involving two points.
Question 2
True or False: The instantaneous rate of change is given by a derivative.
- True
- False
💡 Hint: Recall how derivatives define slopes.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the function f(x) = -2x^2 + 4x + 1, determine the average rate of change from x = 0 to x = 2, and explain what this means in practical terms.
💡 Hint: Use the average rate of change formula.
Question 2
For the function g(t) = t^3 - 12t + 5, find the instantaneous rate of change at t = 2 and determine its significance.
💡 Hint: Calculate g'(t) first.
Challenge and get performance evaluation